Parametrization of closed surfaces for 3-D shape description
Computer Vision and Image Understanding
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Journal of Mathematical Imaging and Vision - Special issue on topology and geometry in computer vision
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Quarterly of Applied Mathematics - Special issue on current and future challenges in the applications of mathematics
Geometric modeling in shape space
ACM SIGGRAPH 2007 papers
Shape Metrics Based on Elastic Deformations
Journal of Mathematical Imaging and Vision
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IEEE Transactions on Pattern Analysis and Machine Intelligence
Parameterization-invariant shape statistics and probabilistic classification of anatomical surfaces
IPMI'11 Proceedings of the 22nd international conference on Information processing in medical imaging
Geometrically consistent elastic matching of 3D shapes: A linear programming solution
ICCV '11 Proceedings of the 2011 International Conference on Computer Vision
Elastic Geodesic Paths in Shape Space of Parameterized Surfaces
IEEE Transactions on Pattern Analysis and Machine Intelligence
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In this paper we define a new methodology for shape analysis of parameterized surfaces, where the main issues are: (1) choice of metric for shape comparisons and (2) invariance to reparameterization. We begin by defining a general elastic metric on the space of parameterized surfaces. The main advantages of this metric are twofold. First, it provides a natural interpretation of elastic shape deformations that are being quantified. Second, this metric is invariant under the action of the reparameterization group. We also introduce a novel representation of surfaces termed square root normal fields or SRNFs. This representation is convenient for shape analysis because, under this representation, a reduced version of the general elastic metric becomes the simple $\ensuremath{\mathbb{L}^2}$ metric. Thus, this transformation greatly simplifies the implementation of our framework. We validate our approach using multiple shape analysis examples for quadrilateral and spherical surfaces. We also compare the current results with those of Kurtek et al. [1]. We show that the proposed method results in more natural shape matchings, and furthermore, has some theoretical advantages over previous methods.